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An experimental study of the flow of R-134a inside an adiabatic spirally coiled capillary tube
international journal of refrigeration 31 (2008) 970–978
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An experimental study of the flow of R-134a inside an adiabatic spirally coiled capillary tube Mohd. Kaleem Khan, Ravi Kumar*, Pradeep K. Sahoo Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, Uttarakhand 247 667, India
article info
abstract
Article history:
This paper presents an experimental investigation for the flow of R-134a inside an adia-
Received 29 August 2007
batic spirally coiled capillary tube. The effect of various geometric parameters like capillary
Received in revised form
tube diameter, length and coil pitch for different capillary tube inlet subcoolings on the
9 January 2008
mass flow rate of R-134a through the spiral capillary tube geometry has been investigated.
Accepted 13 January 2008
It has been established that the coil pitch significantly influences the mass flow rate of R-
Published online 3 February 2008
134a through the adiabatic spiral capillary tube. The effect of providing pressure taps on the capillary tube surface has a negligible effect on the mass flow rate through the capillary
Keywords:
tube. It has been concluded that the effect of coiling of capillary tube reduces the mass flow
R-134a
rate by 5–15% as compared to those of the straight capillary tube operating under similar
Refrigerant
conditions. The data obtained from the experiments are analyzed and a semi-empirical
Capillary
correlation has been developed. The proposed correlation predicts more than 91% of the
Adiabatic
mass flow rate which is in agreement with measured data in an error band of 10%. ª 2008 Elsevier Ltd and IIR. All rights reserved.
Flow Pitch Correlation
Etude expe´rimentale sur l’e´coulement de R-134a a` l’inte´rieur d’un capillaire adiabatique en spirale Mots cle´s : R-134a ; Frigorige´ne ; Capillaire ; Adiabatique ; E´coulement ; Inclinaison ; Corre´lation
1.
Introduction
Capillary tubes are being used as an expansion device in the low capacity refrigerating machines like domestic refrigerators and window type room air conditioners. These are narrow drawn copper tubes of 0.5–2.0 mm bore and 2–6 m length. Owing to the simplicity, low cost, zero maintenance and requirement of a low starting torque motor to run the compressor, capillary tubes have been used in a variety of vapour compression
systems. The various flow aspects of the capillary tube were investigated by a number of researchers since past six decades. Bolstad and Jordan (1948) pioneered the investigations on capillary tubes. They studied the effect of oil entrainment on the mass flow rate through the capillary tube. It was found that the use of oil separator in the system decreases the flow rate by 8% in comparison to that when no oil separator was used. Mikol (1963) carried out an extensive experimental investigation on the capillary tube to explore the various flow phenomena like
* Corresponding author. Tel.: þ91 1332 285740; fax: þ91 1332 285665. E-mail address: [email protected] (R. Kumar). 0140-7007/$ – see front matter ª 2008 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.01.008
international journal of refrigeration 31 (2008) 970–978
Nomenclature cp d DTsub e L M m N P p T v
specific heat at constant pressure (J kg1 K1) capillary tube internal diameter (m) degree of subcooling ( C) roughness height (m) capillary tube length (m) number of repeating variables mass flow rate (kg s1) total number of variables pressure (Pa) coil pitch (m) temperature ( C) specific volume (m3 kg1)
Greek letters m viscosity (kg m1 s1) r density (kg m3) Subscripts in capillary tube inlet f liquid
metastability and choking. They developed a friction factor correlation by flowing water through the same capillary tube. The effect of coiling on the refrigerant mass flow rate of the refrigerant has been discussed by a few investigators. Kuehl and Goldschmidt (1990) have conducted experiments on the flow of R-22 through adiabatic capillary tubes of straight and coiled geometries. They have concluded that because of the coiling of capillary tube, the refrigerant mass flow rate was reduced by not more than 5%. Kim et al. (2002) have studied the flow of R-22 and its alternatives, viz., R-407C and R-410A through the straight and helically coiled adiabatic capillary tubes. They have observed 9% reduction in refrigerant mass flow rate through a coiled tube in comparison to that in straight tube of same length. Zhou and Zhang (2006a) conducted an experimental investigation on helically coiled capillary tubes for the flow of refrigerant R-22. In addition, a numerical model using Mori and Nakayama friction factor correlation (Mori and Nakayama, 1967) was also proposed. It was concluded that for the mean coil diameter beyond 300 mm, the change in mass flow rate was insignificant. It was also observed that the refrigerant mass flow rate through a helical capillary tube with coil diameter of 40 mm was approximately 10% less than that of the straight capillary tube. Further, Zhou and Zhang (2006b) confirmed the hysteresis in refrigerant mass flow rate with increasing and decreasing inlet subcooling in an adiabatic helical capillary tube. The hysteresis effect was more prominent in helical capillary tube than that in straight tube due to the disturbance generated from the secondary flows caused by the centrifugal force. It was also found that in the coiled capillary tube the refrigerant flashed earlier with decreased coil diameter as reduction in coil diameter caused the pressure drop to increase. However, for validation of the numerical model with the experimental data, the increasing subcooling data should be taken into account due to their consistency and reproducibility. A recently published literature on coiled adiabatic capillary by Park et al. (2007) for the flow of R-22 and its alternatives, R-407C and
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R-410A, has revealed a slightly higher drop in mass flow rates of the coiled capillary tubes compared to those in straight capillary tubes as reported by Kim et al. (2002) and Zhou and Zhang (2006a). It was found by Park et al. (2007) that the mass flow rate of the coiled capillary tubes was decreased by 5–16% in comparison to that for the straight capillary tubes. They also proposed a generalized mass flow rate correlation for helically coiled capillary tubes based on Buckingham-p theorem. In addition, a numerical model based on homogenous two-phase flow model was presented using Ito (1959) friction factor correlation for single phase flow and Giri’s equation for two-phase flow (Gorasia et al., 1991). Valladares (2007) also presented a numerical simulation model for the coiled capillary tubes based on the finite volume formulation. The solution was carried out using an implicit step-by-step numerical scheme. The calculation of mass flow rate was made iteratively using Newton–Raphson Algorithm. The experimental studies on spiral capillary tubes are not available in the literature. However, only Khan et al. (2007) have proposed a numerical model for the computation of length of adiabatic spiral capillary tube. It has been found that because of coiling the length of the capillary tube is reduced considerably for a given set of input conditions. Previous researchers have also proposed a number of correlations to predict the refrigerant flow rate for a given capillary tube. For instance, correlations for the mass flow rate of different refrigerants proposed by Wolf et al. (1995) are available in ASHRAE Handbook (2006). Another important study regarding the flow of newer refrigerants inside capillary tubes has been carried out by Melo et al. (1999). They proposed separate correlations for R-12, R-134a and R-600a and a combined mass flow rate correlation for all three refrigerants for the flow inside an adiabatic capillary tube. Choi et al. (2003) have proposed new dimensionless parameters and developed a correlation for the prediction of mass flow rate through the capillary tubes. Since, experimental data for the flow of R-134a refrigerants through spiral capillary tube are not available in the literature, an experimental investigation has been undertaken to study the flow of R-134a through a spiral capillary tube.
2.
Experimental set-up and procedure
The schematic diagram of a experimental set-up has been shown in Fig. 1. The test-section (1) was a copper capillary tube, in which the refrigerant expands from high pressure side to low pressure side. The spirally coiled tube’s testsection in the experimental apparatus was put in horizontal position. From capillary tube refrigerant entered the evaporator (2) consisting of a copper coil submerged in a water tank. A 5.0 kW capacity electric heater (3) was fitted in the evaporator tank to provide heat load to evaporator. The heating load was varied through a variac (4). An agitator (5) was also provided in the tank to maintain the uniform bulk temperature of water. The vapors emerging from the evaporator were sent to liquid accumulator (6) in order to avoid liquid refrigerant to enter the compressor (7). The compressor (7) was run by means of three phase electric motor (8) using belt and pulley type arrangement. The high pressure superheated vapors emerging from
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CHILLER UNIT
20 17
19 21
R3
R2
R1
DR
15
13
16
27
18 12
14 To drain 10 11
22
25
from main watersupply
TEST SECTION
26 9
3
7
5
8
2 6
23 24
4
1.Test-section 2.Evaporator 3.Evaporator heater 4.Variac 5.Agitator 6.Liquid Accumulator 7.Compressor 8.Electric motor 9.Oil separator 10.Water-cooled condenser 11.Condenser water pump12.Receiver 13.Drier-cum-filter 14.Rotameters 15.Subcooler 16.Chiller’s hermetic compressor 17.Air-cooled condenser 18.Chilled water pump 19.Preheater 20.Variac 21.Sight glass 22.Expansion valve (hand-operated) 23.Hand shut-off valves 24.Thermocouple 25.Pressure header 26.Pressure gauge 27. Pressure Transducer Fig. 1 – General layout of the experimental set-up.
the compressor entered through the oil separator (9). After several trial runs, the visual inspection from the sight glass revealed no trace of oil. As an additional check, the capillary tube was tear open and the inside surface was rubbed with white absorbent paper. Again, there was no trace of oil. The oil free vapors from separator (9) were condensed in the water cooled condenser (10). The cooling water was circulated in the condenser by means of a centrifugal pump (11). The high pressure saturated liquid from condenser was collected in a receiver (12) to ensure a continuous supply of refrigerant to the capillary tube. The unwanted solid particles and moisture in refrigerant were removed through drier-cum-filter (13). The bank of four rotameters (14) with one digital rotameter (DR) and three float type rotameters (R1, R2 and R3) of different ranges was installed after the drier-cum-filter. The mass
flow rate data have been acquired by digital rotameter (DR) whereas other three rotameters were placed in parallel to cross verify the mass flow rate measured by digital rotameter. A refrigerant subcooler (15) was provided after the rotameters. The chilled water to the subcooler was supplied by means of a separate chiller unit based on the vapour compression cycle with R-22 as a working fluid. The chiller consisted of a hermetically sealed compressor (16), an air cooled condenser (17), and a tank for cooling water. A centrifugal pump (18) was used to circulate chilled water through the subcooler (15). To vary the degree of subcooling at the capillary tube inlet, a preheater (19) followed the subcooler (15). In the preheater, resistance heating of tube carrying the refrigerant was done and the heat input was controlled by a variac (20). A sight glass (21) was provided after the preheater to visualize the state of
international journal of refrigeration 31 (2008) 970–978
above procedure was repeated till the curve reached the disc periphery. The step-by-step procedure of generating spiral has been shown in Fig. 2(a). The relation between the offset distance and the pitch of spiral is as follows:
refrigerant flow. A hand operated expansion valve (22) was also provided after the condenser (10) to control the refrigerant flow rate in capillary tube by bypassing the excess refrigerant. A number of hand shut-off valves (23) were provided in between the major components of the experimental setup, in case of leak or repair; the damaged component could be retrieved with ease. The temperature at different locations of the set-up and the test-section was measured by means of copper–constantan (T-type) thermocouples (24) while the pressure of the refrigerant was measured with pressure gauges (26) as well as pressure transducers (27) using pressure headers (25). A total of four pressure headers were used in the set-up of which three are shown in Fig. 1. Further, the pressure at the suction and discharge of the compressor were measured with separate bourdon tube pressure gauges. Spiral tube test-section was formed by first producing spiral groove of required pitch on the face of the wooden discs of 600 mm in diameter and 50 mm thickness. Making of a spiral required two points ‘c1’ and ‘c2’ offset by a distance of ‘x’ mm. With the help of a compass, a semicircle of ‘x’ mm radius was drawn taking ‘c1’ as centre and another inverted semicircle of twice the offset distance (i.e., 2x) taking ‘c2’ as centre. The
p ¼ 2x
(1)
Once the spiral was marked on the disc, with the help of mortise chisel a groove large enough to accommodate the capillary tube of 1.63 mm (ID) was carved out of the disc. The process of carving out of spiral required high degree of workmanship. Fig. 2(b) shows three wooden discs having spiral grooves of three different pitches, viz., 20 mm, 40 mm and 60 mm. A hole of 25 mm size was drilled at the centre of the each disc so as to facilitate the capillary tube to pass through the disc. After generating groove on the disc, the capillary tube of a given diameter was embedded into the groove and clips were used to contain the tubes inside the groove. The testsection was insulated by putting a thick layer of ceramic wool on the test-section. Moreover, an aluminium sheet was fixed around the periphery to house the ceramic wool insulation. The final arrangement of spiral test-section has been
p c2
c1
c2 c1
c2 c1
x
I
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I
III
c2 c1
c2 c1
c2 c1
IV
V
VI
a
(iii)
(ii) (i)
b Fig. 2 – (a) Step-by-step procedure for generating spiral. (b) Spiral patterns for three pitches: (i) 20 mm (ii) 40 mm, and (iii) 60 mm.
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international journal of refrigeration 31 (2008) 970–978
Ø600
Ø6.35
Ø1.52
25 Ø0.25
Ø6.35
40
Thermocouple
Pressure Tap
Fig. 3 – Schematic diagram of the test-section.
shown in Fig. 3. Three pitches for three capillary tube diameters were used to investigate the flow of R-134a inside the spirally coiled geometry of capillary tube. Three different wooden circular discs of 600 mm diameter were used for different coil pitches. To elaborate it further, the capillary tube of a given diameter and length 6.4 m was taken. In order to measure the pressure along the capillary tube, 15 taps at a gap of 40 mm have been provided on the length of capillary tube. ‘T-joint’, also shown in Fig. 3, was brazed on the capillary tube to house the aperture on the capillary tube surface. Then, the capillary tube with T-joints brazed over the taps was fixed in the spiral groove of the given wooden cylindrical disc by means of a number of clips. The fabrication of ‘T-joint’ required good workmanship as during brazing of T-joint a controlled heating of the tapped zone was required otherwise tube was blocked. And it is because of this the brazing was done a distance away from the aperture using T-joints. The aperture or pressure tap is produced by weakening the wall of capillary tube by
a smooth round file. The weakened zone was subjected to piercing by the sharp tip of a needle. The process described for generating pressure taps was first employed by Bolstad and Jordan (1948). Instead of piercing the capillary tube, they employed drilling operation to produce the hole on the capillary surface. The tap diameter as measured by microscope was approximately 0.25 mm with an accuracy of 0.01 mm. The capillary tube with pressure taps generated on its surface was termed as instrumented capillary tube while the tube without pressure taps was known as non-instrumented capillary tube. A total of 14 test-sections were used in the present experimental study, the details of capillary tube and range of operating parameters have been shown in Table 1. For spiral geometry nine instrumented test-sections and one noninstrumented test-section of 1.4 mm capillary diameter and 40 mm coil pitch whereas for straight geometry three instrumented test-sections and one non-instrumented test-section of 1.4 mm capillary tube diameter were used in the present experimental investigation. Initially, the capillary tube of a given diameter and length 6.4 m was taken. A total of six lengths for each test-section were investigated. Each length is obtained by cutting the capillary tube by 0.8 m. For each length, the degree of subcooling at the capillary tube inlet was controlled by the subcooler and the preheater together. For a particular capillary length, 4–5 subcoolings were obtained in the range of 0–20 C. The mass flow rate corresponding to each level of inlet subcooling was recorded. The pressure at capillary inlet for all experimental runs was maintained constant at 740 kPa. The internal surface roughness of the capillary tubes was measured using Surface Profilometer. For the measurement of surface roughness, a piece of capillary tube was sliced into two halves. The roughness for the capillary tubes of diameters 1.12 mm, 1.40 mm and 1.63 mm was found to be 7.05 mm, 6.22 mm and 3.58 mm, respectively. The capillary tube diameters and the pressure tap diameters were measured with the help of Tool maker’s microscope. The internal diameters of the capillary tubes are 1.12 mm, 1.40 mm and 1.63 mm, respectively. The uncertainty in the measurement of capillary tube diameters was 0.01 mm, capillary tube lengths 0.1 mm and surface roughness is 0.01 mm. Similarly, uncertainties in the measurement of pressure was 3.5 kPa in case of pressure gauges and 0.25% full scale (2.6 kPa) in case of pressure transducers while uncertainty in the measurement of temperature using T-type thermocouple was 0.1 C. The uncertainty in the
Table 1 – Range of input parameters Parameters
Selected range Straight capillary tube Instrumented
d (mm) L (m)a e/d p (mm) DTsub ( C) Pin (kPa)
1.12, 1.40, 1.63 6.4–2.4 0.0063, 0.0044, 0.0022 – 0–20 740
Non-instrumented 1.40 6.4–2.4 0.0044 – 0–20 740
Spiral capillary tube Instrumented 1.12, 1.40, 1.63 6.4–2.4 0.0063, 0.0044, 0.0022 20, 40, 60 0–20 740
a A total of six capillary lengths, viz., 6.4 m, 5.6 m, 4.8 m, 4.0 m, 3.2 m, 2.4 m, have been used for each test-section.
Non-instrumented 1.40 6.4–2.4 0.0044 40 0–20 740
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international journal of refrigeration 31 (2008) 970–978
Results and discussion
First of all, a comparison of experimental results of straight capillary tube with the correlation of Melo et al. (1999) has been made to check the integrity of the experimental set-up. Melo et al. (1999) correlation for mass flow rate of R-134a is given below: p0:552 p0:178 p5 ¼ 0:125p0:460 1 2 3
A comparison of experimental results of straight capillary tube has been made with those predicted by the widely accepted Melo et al. (1999) correlation to establish the integrity of present experimental set-up. Fig. 4 has been drawn taking measured experimental refrigerant mass flow rate in a straight capillary tube as abscissa and that predicted by Melo et al. (1999) correlation for the present experimental input conditions as ordinate. It has been found that Melo et al. (1999) correlation overpredicts the experimental data of both instrumented (with pressure taps) and non-instrumented (without pressure taps) straight capillary tubes in an error band of 0 to þ20%. Further, more than 75% data are in agreement with Melo et al. (1999) correlation in the error band of 0 to þ15%. It is to be noted that Melo et al. (1999) correlation has predicted their own experimental data in an error band of 15%. Therefore, it can be concluded that the data acquired from the present experimental set-up are in good agreement with predictions of Melo et al. (1999) correlation. This establishes the integrity of experimental set-up. In order to show the effect of pressure taps on the mass flow rate, the results of straight and spiral capillary instrumented and non-instrumented capillary tubes have been shown in Fig. 5. It is observed that the provision of taps for the measurement of pressure does not have any significant effect on the mass flow rate through the capillary tube as the deviation in mass flow rate in instrumented is less than 1%. The uncertainty in the refrigerant flow measurement is also 1%. Therefore, any conclusion regarding the effect of pressure taps on the refrigerant mass flow rate cannot be drawn. The
20 15 10
Length, L, m 5
6.4 5.6 4.8 4.0 3.2 2.4
non-instrumented instrumented
25 Pin d p e
20
spiral
740 kPa 1.40 mm 40 mm 6.22 μm
15 10 Length, L, m 5
6.4
5.6
4.8 4.0
3.2
2.4
non-instrumented instrumented
0 0
5
10
15
20
25
inlet subcooling, Tsub, °C Fig. 5 – Comparison of the mass flow rate for straight and coiled instrumented and non-instrumented capillary tubes.
insignificant effect of pressure taps on mass flow rate is due to the fact that the pressure tap area is very small in comparison to the internal surface area of the capillary tube and the flow passes near the taps almost undisturbed as a flexible boundary is formed at the location of tap as the refrigerant in the lines connecting taps to pressure header is stagnant. Since, cut-and-try method has been employed to carry out the investigation, for each cut of length, the corresponding mass flow rate has been recorded for different inlet subcoolings. Fig. 6 has been drawn with length of capillary as abscissa
40
25 coil pitch, mm
+20%
mass flow rate, m, kg h-1
predicted mass flow rate, kg h-1
straight Pin 740 kPa d 1.40 mm e 6.22 μm
0
(2)
mass flow rate, m, kg h-1
3.
25
mass flow rate, m, kg h-1
measurement of mass flow rate was 1% full scale (0.5 kg h1). All the instruments were calibrated prior to installation.
30
20
instrumented (with pressure taps) non-instrumented ( without pressure taps)
10
0
20 40 60 straight
20
15 d = 1.63 mm 10
d = 1.40 mm d = 1.12 mm
5
0 0
10
20
30
40
measured mass flow rate, kg h-1 Fig. 4 – Comparison of mass flow rate predicted by Melo et al. (1999) correlation with the measured mass flow rate.
2
3
4
5
6
capillary tube length, L, m Fig. 6 – Effect of coil pitch and capillary tube length on refrigerant mass flow rate.
7
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international journal of refrigeration 31 (2008) 970–978
and refrigerant mass flow rate as ordinate for the inlet subcoolings of refrigerant being in the range of 0–0.5 C. For the sake of comparison the straight tube data have also been plotted. The refrigerant mass flow rate rises with the increase in coil pitch and becomes highest for straight capillary tube. The best fit lines for straight and 20 mm pitch spiral capillary tubes have been drawn to quantify the effect of coiling. It has been observed that the mass flow rate is reduced in the range of 5–10% for all lengths of capillary tube. In fact, the coiling effect is pronounced for higher capillary tube diameters. The reason for the increase in mass flow rate with the increasing coil pitch is that increasing pitch leads to straightening of the capillary tube. The mass flow rate is highest for straight capillary tube as the straight capillary tube offers least resistance to the refrigerant flow. Further, it can be seen from the figure that the refrigerant mass flow rate increases with
reduction in capillary tube length, i.e., when the length is reduced from 6.4 m to 2.4 m, the mass flow rate is increased by 45%, 55% and 60% for tube diameters of 1.12 mm, 1.40 mm and 1.63 mm, respectively. Also, the mass flow rate increases tremendously with the small increase in tube diameter, i.e., as the tube diameter is increased from 1.12 mm to 1.63 mm, the mass flow is increased by 150% and 180% for capillary lengths of 6.4 m and 2.4 m, respectively. As per Darcy– Weisbach equation for pipe flow (Douglas et al., 1995), the pressure drop in a pipe is directly proportional to pipe length and inversely proportional to fifth power of pipe diameter. This fact also finds agreement with the experimental results. The cumulative effect of coil pitch, capillary tube diameter, the inlet subcooling and capillary tube length on the refrigerant mass flow rate has been presented in Fig. 7. It can be observed that with a slight increase in capillary tube diameter,
40
40 20 60
30
L = 6.4 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
coil pitch, mm 40 straight
d = 1.63 mm
20
d = 1.40 mm
10
d = 1.12 mm 0
coil pitch, mm 20 60
30
20
d = 1.63 mm d = 1.40 mm
10
d = 1.12 mm 0
0
5
10
15
20
25
0
5
inlet subcooling, ΔTsub,°C
15
20
25
40 coil pitch, mm 20 60
30
L = 4.8 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
10
inlet subcooling, ΔTsub,°C
40 40 straight
20
d = 1.63 mm d = 1.40 mm
10 d = 1.12 mm 0
coil pitch, mm 30
L = 4.0 m
40 straight
20 60
d = 1.63 mm 20 d = 1.40 mm 10 d = 1.12 mm 0
0
5
10
15
20
0
25
5
inlet subcooling, ΔTsub,°C
10
15
20
25
inlet subcooling, ΔTsub,°C
40
40 coil pitch, mm 20 60
30
L = 3.2 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
L = 5.6 m
40 straight
40 straight d = 1.63 mm
20 d = 1.40 mm 10 d = 1.12 mm
coil pitch, mm 20 60
30
L = 2.4 m
40 straight
d = 1.63 mm
20 d = 1.40 mm 10
d = 1.12 mm
0
0 0
5
10
15
20
inlet subcooling, ΔTsub,°C
25
0
5
10
15
20
inlet subcooling, ΔTsub,°C
Fig. 7 – Variation of mass flow rate with capillary length, diameter, pitch and inlet subcooling.
25
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international journal of refrigeration 31 (2008) 970–978
In the above equation, the total number of variables is nine (N ¼ 9), out of which four variables, viz., d, rf, mf and cp are fixed as repeating variables, i.e. (M ¼ 4). Buckingham-p theorem (Douglas et al., 1995) states that the number of non-dimensional p-terms will be the difference between the total number of
Table 2 – Non-dimensional parameters p-Group Definition Description Relative uncertainty ðdp pÞ p1
d2 rf Pin m2f
p2
L Geometry effect d d2 r2f cp DTsub Inlet subcooling m2f
0.1564
p4
p d
Effect of coiling
0.0071
p5
m dmf
Mass flow rate
p3
Inlet pressure
0.0176
0.0186
parameters and the number of repeating variables, i.e. (N M ¼ 5). By performing the dimensional analysis, all the five p-terms and uncertainties associated with each p-term have been mentioned in Table 2. Eq. (3) in non-dimensional form can be represented as follows: p5 ¼ f2 ðp1 ; p2 ; p3 ; p4 Þ
(4)
Eq. (4) can be further expressed in a non-linear power law form as p5 ¼ Cpc11 pc22 pc33 F
(5)
where C is a constant and F is the coiling factor. Regression analysis of 275 data sets of coiled capillary tube and 103 data sets of straight capillary tube has resulted into the following correlation: p0:503 p0:126 F p5 ¼ Cp0:464 1 2 3
(6)
For straight capillary tube C ¼ 0.3478, F ¼ 1 and for spiral . capillary tube C ¼ 0.2607 and F ¼ p0:0393 4 In order to compare the predicted mass flow rate by the proposed correlation with the measured mass flow rate, Fig. 8 has been drawn. The mass flow rate predicted by Eq. (6) is in good agreement with the experimental mass flow rate as 85% of the straight capillary tube mass flow rate data lies in an error band of 10%. While, in case of coiled tube the same correlation predicts 90% of the mass flow rate in the error band of 10%. In Fig. 9, the proposed correlation for straight capillary tube has been compared with already established correlations of Melo et al. (1999) and Wolf et al. (1995). Melo et al. (1999) correlation has already been shown in Eq. (2). Wolf et al. (1995) correlation for R-134a (30 data sets) with 5% agreement with their own experimental data given by p5 ¼ 0:0129ðp1 Þ0:492 ðp2 Þ0:387 ðp3 Þ0:187
(7)
The percentage deviation appearing in Fig. 9 is evaluated using the following equation: percentage deviation ¼
mpredicted mmeasured 100 mmeasured
(8)
Fig. 9 shows the deviation of mass flow rates predicted by Melo et al. (1999) correlation, Wolf et al. (1995) correlation and the 40
predicted mass flow rate, kg h-1
the refrigerant mass flow rate increases drastically. At 10 C inlet subcooling, when the diameter is increased from 1.12 mm to 1.63 mm the refrigerant mass flow rate is increased in range of 170 5% for all capillary tube lengths. At the same inlet subcooling of 10 C, as the capillary length is reduced from 6.4 m to 2.4 m, the refrigerant mass flow rate is increased in the range of 50 5% for all tube diameters. Similarly, if the inlet subcooling is increased from 0 C to 10 C, the refrigerant mass flow rate is increased in a range 45 2% for all capillary tube diameters, lengths and pitches. In fact, the length of liquid region increases with the rise in inlet subcooling. Since the pressure drop is less in liquid region as compared to that in the twophase region, the refrigerant mass flow rate increases with the rise in inlet subcooling. The refrigerant mass flow rate also increases with the coil pitch. It has been observed that lower the pitch lesser will be the refrigerant mass flow rate. For 10 C inlet subcooling, the refrigerant mass flow rate for 20 mm, 40 mm and 60 mm spiral capillary tubes in comparison to the straight capillary tube is reduced in a range of 5– 15%. This is due to the fact that friction factor decreases with the increase in coil pitch and is least for the straight tube. Furthermore, increasing the coil pitch reduces the curvature thereby decreasing the resistance to the refrigerant flow. All the available correlations in the literature are mostly derived for straight capillary tubes. The mass flow rate of refrigerant through the adiabatic spiral capillary tube depends upon the capillary tube diameter, length, coil pitch, roughness and the inlet subcooling. As the capillary tubes are available in a limited band of roughness, the roughness effect is ignored in the development of correlation. Therefore, the roughness is not considered in the development of the correlation. Other parameters like inlet pressure, the density, the viscosity and specific heat of the refrigerant have also an influence on the mass flow rate. The REFPROP 7.0 database (McLinden et al., 2002), has been used to determine the thermodynamic and transport properties of the refrigerant R-134a, appearing in Eq. (3). The mass flow rate can be represented as a function of all these parameters (3) m ¼ f1 Pin ; L; d; p; DTsub ; rf ; mf ; cp
+10
35 30
-10 25 20 15 10 straight spiral
5 0 0
5
10
15
20
25
30
35
measured mass flow rate, kg h-1 0.0133
Fig. 8 – Comparison of the predicted mass flow rate with the measured experimental mass flow rate.
40
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international journal of refrigeration 31 (2008) 970–978
pressure taps on the refrigerant mass flow rate in straight and spiral capillary tube as well. 2. Parametric study has been conducted for the mass flow rate of R-134a through the capillary tubes of straight and coiled geometry. The effect coiling on refrigerant causes the refrigerant mass flow rate to reduce by 5–15%. 3. The semi-empirical correlations to predict the refrigerant mass flow rate through straight as well as spiral capillary tube have been proposed.
percentage deviation, %
60 40 20 0 -20 proposed correlation Melo et al. [15] correlation Wolf et al. [19] correlation
-40
references
-60 0
5
10
15
20
25
30
35
40
measured mass flow rate, kg h-1 Fig. 9 – Comparison of the proposed correlation with Melo et al. (1999) and Wolf et al. (1995) correlations.
proposed correlation from the measured experimental mass flow rate. The refrigerant mass flow rate predicted by Melo et al. (1999) correlation lies in the error band of 0 to þ20%. Melo et al. (1999) correlation has been developed for range of operating parameters different from the present experimental investigation. The range of tube diameter for Melo et al. (1999) correlation is 0.66–1.05 mm while in the present case it is 1.12– 1.63 mm, range of length is 1.99–3.02 m while in this case it is 2.4–6.4 m and range of inlet subcooling is 0–16 C, whereas, for the present case it is 0–25 C. The range of inlet pressure for Melo et al. (1999) correlation is 900 kPa and 1100 kPa while in the present study the inlet pressure has been kept nearly constant at 740 kPa. Most importantly it is the internal tube roughness, which is really making this difference. The capillary tube internal tube roughness as used by Melo et al. (1999) experiments lies in the range of 0.7–1.1 mm, whereas, in the present case the roughness is in the range of 3.5– 7.1 mm was in the tube. Therefore, with such a large difference in the range of operating parameters overprediction of 5% is a fairly good proposition. Also, the present experimental investigation has been carried out on both instrumented and non-instrumented straight capillary tubes whereas Melo et al. (1999) correlation has been developed for non-instrumented straight capillary tube. On the other hand Wolf et al. (1995) correlation predicts the same in the error band of þ10 to þ38%. Such a large discrepancy may be because of the fact that Wolf et al. (1995) has been developed for four different refrigerants R-134a, R-22, R-410a and R-152a with only 30 data points of R-134a used in the development of Wolf et al. (1995) correlation.
4.
Conclusions
The following conclusions can be drawn from the present study: 1. The effect of taps on the mass flow rate through the capillary tube is insignificant. Virtually, there is no effect of
ASHRAE Handbook – Refrigeration, 2006. American Society of Heating, Refrigerating and Air-Conditioning Engineer Inc., p 26 (Chapter 44). Bolstad, M.M., Jordan, R.C., 1948. Theory and use of the capillary tube expansion device. Refrigerating Engineering, 519–523. Choi, J., Kim, Y., Kim, H.Y., 2003. A generalized correlation for refrigerant mass flow rate through adiabatic capillary tubes. International Journal of Refrigeration 26, 881–888. Douglas, J.F., Gasiorek, J.M., Swaffield, J.A., 1995. Fluid Mechanics. Addison-Wesley Longman Inc., Edinburgh, UK, 299 pp. Gorasia, J.N., Dubey, N., Jain, K.K., 1991. Computer aided design of capillaries of different configurations. ASHRAE Transactions (Part 1), 132–138. Ito, H., 1959. Friction factors for turbulent flow in curved pipes. Journal of Basic Engineering D81, 123–134. Kuehl, S.J., Goldschmidt, V.W., 1990. Steady flows of R-22 through capillary tubes: test data. ASHRAE Transactions, 719–728. Kim, S.G., Ro, S.T., Kim, M.S., 2002. Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners. International Journal of Refrigeration 25, 521–531. Khan, M.K., Kumar, R., Sahoo, P.K., September 2007. Flow characteristics of refrigerants flowing inside an adiabatic spiral capillary tube. HVAC&R Research ASHRAE 13 (5), 731–748. Mikol, E.P., 1963. Adiabatic single and two-phase flow in small bore tubes. ASHRAE Journal, 75–86. Mori, Y., Nakayama, W., 1967. Study on forced convective heat transfer in curved pipes (2nd report, turbulent region). International Journal of Heat Mass Transfer 10, 37–59. Melo, C., Ferreira, R.T.S., Neto, C.B., Goncalves, J.M., Mezavila, M. M., 1999. An experimental analysis of adiabatic capillary tube. Applied Thermal Engineering 19, 669–684. McLinden, M.O., Klein, S.A., Lemmon, E.W., 2002. REFPROPversion 7 – thermodynamic and transport properties of refrigerants and refrigerant mixtures. NIST Standard Reference Database. Park, C., Lee, S., Kang, H., Kim, Y., 2007. Experimentation and modeling of refrigerant flow through coiled capillary tube. International Journal of Refrigeration 30, 1168–1175. Valladares, G., 2007. Numerical simulation and experimental validation of coiled adiabatic capillary tubes. Applied Thermal Engineering 27, 1062–1071. Wolf, D.A., Bittle, R.R., Pate, M.B., 1995. Adiabatic capillary tube performance with alternative refrigerants. ASHRAE Research Project RP-762. Zhou, G., Zhang, Y., 2006a. Numerical and experimental investigations on the performance of coiled adiabatic capillary tube. Applied Thermal Engineering 26, 1106–1114. Zhou, G., Zhang, Y., 2006b. Experimental investigation on hysteresis effect of refrigerant flowing through a coiled adiabatic capillary tube. Energy Conversion and Management 47, 3084–3093.
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An experimental study of the flow of R-134a inside an adiabatic spirally coiled capillary tube Mohd. Kaleem Khan, Ravi Kumar*, Pradeep K. Sahoo Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, Uttarakhand 247 667, India
article info
abstract
Article history:
This paper presents an experimental investigation for the flow of R-134a inside an adia-
Received 29 August 2007
batic spirally coiled capillary tube. The effect of various geometric parameters like capillary
Received in revised form
tube diameter, length and coil pitch for different capillary tube inlet subcoolings on the
9 January 2008
mass flow rate of R-134a through the spiral capillary tube geometry has been investigated.
Accepted 13 January 2008
It has been established that the coil pitch significantly influences the mass flow rate of R-
Published online 3 February 2008
134a through the adiabatic spiral capillary tube. The effect of providing pressure taps on the capillary tube surface has a negligible effect on the mass flow rate through the capillary
Keywords:
tube. It has been concluded that the effect of coiling of capillary tube reduces the mass flow
R-134a
rate by 5–15% as compared to those of the straight capillary tube operating under similar
Refrigerant
conditions. The data obtained from the experiments are analyzed and a semi-empirical
Capillary
correlation has been developed. The proposed correlation predicts more than 91% of the
Adiabatic
mass flow rate which is in agreement with measured data in an error band of 10%. ª 2008 Elsevier Ltd and IIR. All rights reserved.
Flow Pitch Correlation
Etude expe´rimentale sur l’e´coulement de R-134a a` l’inte´rieur d’un capillaire adiabatique en spirale Mots cle´s : R-134a ; Frigorige´ne ; Capillaire ; Adiabatique ; E´coulement ; Inclinaison ; Corre´lation
1.
Introduction
Capillary tubes are being used as an expansion device in the low capacity refrigerating machines like domestic refrigerators and window type room air conditioners. These are narrow drawn copper tubes of 0.5–2.0 mm bore and 2–6 m length. Owing to the simplicity, low cost, zero maintenance and requirement of a low starting torque motor to run the compressor, capillary tubes have been used in a variety of vapour compression
systems. The various flow aspects of the capillary tube were investigated by a number of researchers since past six decades. Bolstad and Jordan (1948) pioneered the investigations on capillary tubes. They studied the effect of oil entrainment on the mass flow rate through the capillary tube. It was found that the use of oil separator in the system decreases the flow rate by 8% in comparison to that when no oil separator was used. Mikol (1963) carried out an extensive experimental investigation on the capillary tube to explore the various flow phenomena like
* Corresponding author. Tel.: þ91 1332 285740; fax: þ91 1332 285665. E-mail address: [email protected] (R. Kumar). 0140-7007/$ – see front matter ª 2008 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.01.008
international journal of refrigeration 31 (2008) 970–978
Nomenclature cp d DTsub e L M m N P p T v
specific heat at constant pressure (J kg1 K1) capillary tube internal diameter (m) degree of subcooling ( C) roughness height (m) capillary tube length (m) number of repeating variables mass flow rate (kg s1) total number of variables pressure (Pa) coil pitch (m) temperature ( C) specific volume (m3 kg1)
Greek letters m viscosity (kg m1 s1) r density (kg m3) Subscripts in capillary tube inlet f liquid
metastability and choking. They developed a friction factor correlation by flowing water through the same capillary tube. The effect of coiling on the refrigerant mass flow rate of the refrigerant has been discussed by a few investigators. Kuehl and Goldschmidt (1990) have conducted experiments on the flow of R-22 through adiabatic capillary tubes of straight and coiled geometries. They have concluded that because of the coiling of capillary tube, the refrigerant mass flow rate was reduced by not more than 5%. Kim et al. (2002) have studied the flow of R-22 and its alternatives, viz., R-407C and R-410A through the straight and helically coiled adiabatic capillary tubes. They have observed 9% reduction in refrigerant mass flow rate through a coiled tube in comparison to that in straight tube of same length. Zhou and Zhang (2006a) conducted an experimental investigation on helically coiled capillary tubes for the flow of refrigerant R-22. In addition, a numerical model using Mori and Nakayama friction factor correlation (Mori and Nakayama, 1967) was also proposed. It was concluded that for the mean coil diameter beyond 300 mm, the change in mass flow rate was insignificant. It was also observed that the refrigerant mass flow rate through a helical capillary tube with coil diameter of 40 mm was approximately 10% less than that of the straight capillary tube. Further, Zhou and Zhang (2006b) confirmed the hysteresis in refrigerant mass flow rate with increasing and decreasing inlet subcooling in an adiabatic helical capillary tube. The hysteresis effect was more prominent in helical capillary tube than that in straight tube due to the disturbance generated from the secondary flows caused by the centrifugal force. It was also found that in the coiled capillary tube the refrigerant flashed earlier with decreased coil diameter as reduction in coil diameter caused the pressure drop to increase. However, for validation of the numerical model with the experimental data, the increasing subcooling data should be taken into account due to their consistency and reproducibility. A recently published literature on coiled adiabatic capillary by Park et al. (2007) for the flow of R-22 and its alternatives, R-407C and
971
R-410A, has revealed a slightly higher drop in mass flow rates of the coiled capillary tubes compared to those in straight capillary tubes as reported by Kim et al. (2002) and Zhou and Zhang (2006a). It was found by Park et al. (2007) that the mass flow rate of the coiled capillary tubes was decreased by 5–16% in comparison to that for the straight capillary tubes. They also proposed a generalized mass flow rate correlation for helically coiled capillary tubes based on Buckingham-p theorem. In addition, a numerical model based on homogenous two-phase flow model was presented using Ito (1959) friction factor correlation for single phase flow and Giri’s equation for two-phase flow (Gorasia et al., 1991). Valladares (2007) also presented a numerical simulation model for the coiled capillary tubes based on the finite volume formulation. The solution was carried out using an implicit step-by-step numerical scheme. The calculation of mass flow rate was made iteratively using Newton–Raphson Algorithm. The experimental studies on spiral capillary tubes are not available in the literature. However, only Khan et al. (2007) have proposed a numerical model for the computation of length of adiabatic spiral capillary tube. It has been found that because of coiling the length of the capillary tube is reduced considerably for a given set of input conditions. Previous researchers have also proposed a number of correlations to predict the refrigerant flow rate for a given capillary tube. For instance, correlations for the mass flow rate of different refrigerants proposed by Wolf et al. (1995) are available in ASHRAE Handbook (2006). Another important study regarding the flow of newer refrigerants inside capillary tubes has been carried out by Melo et al. (1999). They proposed separate correlations for R-12, R-134a and R-600a and a combined mass flow rate correlation for all three refrigerants for the flow inside an adiabatic capillary tube. Choi et al. (2003) have proposed new dimensionless parameters and developed a correlation for the prediction of mass flow rate through the capillary tubes. Since, experimental data for the flow of R-134a refrigerants through spiral capillary tube are not available in the literature, an experimental investigation has been undertaken to study the flow of R-134a through a spiral capillary tube.
2.
Experimental set-up and procedure
The schematic diagram of a experimental set-up has been shown in Fig. 1. The test-section (1) was a copper capillary tube, in which the refrigerant expands from high pressure side to low pressure side. The spirally coiled tube’s testsection in the experimental apparatus was put in horizontal position. From capillary tube refrigerant entered the evaporator (2) consisting of a copper coil submerged in a water tank. A 5.0 kW capacity electric heater (3) was fitted in the evaporator tank to provide heat load to evaporator. The heating load was varied through a variac (4). An agitator (5) was also provided in the tank to maintain the uniform bulk temperature of water. The vapors emerging from the evaporator were sent to liquid accumulator (6) in order to avoid liquid refrigerant to enter the compressor (7). The compressor (7) was run by means of three phase electric motor (8) using belt and pulley type arrangement. The high pressure superheated vapors emerging from
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international journal of refrigeration 31 (2008) 970–978
CHILLER UNIT
20 17
19 21
R3
R2
R1
DR
15
13
16
27
18 12
14 To drain 10 11
22
25
from main watersupply
TEST SECTION
26 9
3
7
5
8
2 6
23 24
4
1.Test-section 2.Evaporator 3.Evaporator heater 4.Variac 5.Agitator 6.Liquid Accumulator 7.Compressor 8.Electric motor 9.Oil separator 10.Water-cooled condenser 11.Condenser water pump12.Receiver 13.Drier-cum-filter 14.Rotameters 15.Subcooler 16.Chiller’s hermetic compressor 17.Air-cooled condenser 18.Chilled water pump 19.Preheater 20.Variac 21.Sight glass 22.Expansion valve (hand-operated) 23.Hand shut-off valves 24.Thermocouple 25.Pressure header 26.Pressure gauge 27. Pressure Transducer Fig. 1 – General layout of the experimental set-up.
the compressor entered through the oil separator (9). After several trial runs, the visual inspection from the sight glass revealed no trace of oil. As an additional check, the capillary tube was tear open and the inside surface was rubbed with white absorbent paper. Again, there was no trace of oil. The oil free vapors from separator (9) were condensed in the water cooled condenser (10). The cooling water was circulated in the condenser by means of a centrifugal pump (11). The high pressure saturated liquid from condenser was collected in a receiver (12) to ensure a continuous supply of refrigerant to the capillary tube. The unwanted solid particles and moisture in refrigerant were removed through drier-cum-filter (13). The bank of four rotameters (14) with one digital rotameter (DR) and three float type rotameters (R1, R2 and R3) of different ranges was installed after the drier-cum-filter. The mass
flow rate data have been acquired by digital rotameter (DR) whereas other three rotameters were placed in parallel to cross verify the mass flow rate measured by digital rotameter. A refrigerant subcooler (15) was provided after the rotameters. The chilled water to the subcooler was supplied by means of a separate chiller unit based on the vapour compression cycle with R-22 as a working fluid. The chiller consisted of a hermetically sealed compressor (16), an air cooled condenser (17), and a tank for cooling water. A centrifugal pump (18) was used to circulate chilled water through the subcooler (15). To vary the degree of subcooling at the capillary tube inlet, a preheater (19) followed the subcooler (15). In the preheater, resistance heating of tube carrying the refrigerant was done and the heat input was controlled by a variac (20). A sight glass (21) was provided after the preheater to visualize the state of
international journal of refrigeration 31 (2008) 970–978
above procedure was repeated till the curve reached the disc periphery. The step-by-step procedure of generating spiral has been shown in Fig. 2(a). The relation between the offset distance and the pitch of spiral is as follows:
refrigerant flow. A hand operated expansion valve (22) was also provided after the condenser (10) to control the refrigerant flow rate in capillary tube by bypassing the excess refrigerant. A number of hand shut-off valves (23) were provided in between the major components of the experimental setup, in case of leak or repair; the damaged component could be retrieved with ease. The temperature at different locations of the set-up and the test-section was measured by means of copper–constantan (T-type) thermocouples (24) while the pressure of the refrigerant was measured with pressure gauges (26) as well as pressure transducers (27) using pressure headers (25). A total of four pressure headers were used in the set-up of which three are shown in Fig. 1. Further, the pressure at the suction and discharge of the compressor were measured with separate bourdon tube pressure gauges. Spiral tube test-section was formed by first producing spiral groove of required pitch on the face of the wooden discs of 600 mm in diameter and 50 mm thickness. Making of a spiral required two points ‘c1’ and ‘c2’ offset by a distance of ‘x’ mm. With the help of a compass, a semicircle of ‘x’ mm radius was drawn taking ‘c1’ as centre and another inverted semicircle of twice the offset distance (i.e., 2x) taking ‘c2’ as centre. The
p ¼ 2x
(1)
Once the spiral was marked on the disc, with the help of mortise chisel a groove large enough to accommodate the capillary tube of 1.63 mm (ID) was carved out of the disc. The process of carving out of spiral required high degree of workmanship. Fig. 2(b) shows three wooden discs having spiral grooves of three different pitches, viz., 20 mm, 40 mm and 60 mm. A hole of 25 mm size was drilled at the centre of the each disc so as to facilitate the capillary tube to pass through the disc. After generating groove on the disc, the capillary tube of a given diameter was embedded into the groove and clips were used to contain the tubes inside the groove. The testsection was insulated by putting a thick layer of ceramic wool on the test-section. Moreover, an aluminium sheet was fixed around the periphery to house the ceramic wool insulation. The final arrangement of spiral test-section has been
p c2
c1
c2 c1
c2 c1
x
I
973
I
III
c2 c1
c2 c1
c2 c1
IV
V
VI
a
(iii)
(ii) (i)
b Fig. 2 – (a) Step-by-step procedure for generating spiral. (b) Spiral patterns for three pitches: (i) 20 mm (ii) 40 mm, and (iii) 60 mm.
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international journal of refrigeration 31 (2008) 970–978
Ø600
Ø6.35
Ø1.52
25 Ø0.25
Ø6.35
40
Thermocouple
Pressure Tap
Fig. 3 – Schematic diagram of the test-section.
shown in Fig. 3. Three pitches for three capillary tube diameters were used to investigate the flow of R-134a inside the spirally coiled geometry of capillary tube. Three different wooden circular discs of 600 mm diameter were used for different coil pitches. To elaborate it further, the capillary tube of a given diameter and length 6.4 m was taken. In order to measure the pressure along the capillary tube, 15 taps at a gap of 40 mm have been provided on the length of capillary tube. ‘T-joint’, also shown in Fig. 3, was brazed on the capillary tube to house the aperture on the capillary tube surface. Then, the capillary tube with T-joints brazed over the taps was fixed in the spiral groove of the given wooden cylindrical disc by means of a number of clips. The fabrication of ‘T-joint’ required good workmanship as during brazing of T-joint a controlled heating of the tapped zone was required otherwise tube was blocked. And it is because of this the brazing was done a distance away from the aperture using T-joints. The aperture or pressure tap is produced by weakening the wall of capillary tube by
a smooth round file. The weakened zone was subjected to piercing by the sharp tip of a needle. The process described for generating pressure taps was first employed by Bolstad and Jordan (1948). Instead of piercing the capillary tube, they employed drilling operation to produce the hole on the capillary surface. The tap diameter as measured by microscope was approximately 0.25 mm with an accuracy of 0.01 mm. The capillary tube with pressure taps generated on its surface was termed as instrumented capillary tube while the tube without pressure taps was known as non-instrumented capillary tube. A total of 14 test-sections were used in the present experimental study, the details of capillary tube and range of operating parameters have been shown in Table 1. For spiral geometry nine instrumented test-sections and one noninstrumented test-section of 1.4 mm capillary diameter and 40 mm coil pitch whereas for straight geometry three instrumented test-sections and one non-instrumented test-section of 1.4 mm capillary tube diameter were used in the present experimental investigation. Initially, the capillary tube of a given diameter and length 6.4 m was taken. A total of six lengths for each test-section were investigated. Each length is obtained by cutting the capillary tube by 0.8 m. For each length, the degree of subcooling at the capillary tube inlet was controlled by the subcooler and the preheater together. For a particular capillary length, 4–5 subcoolings were obtained in the range of 0–20 C. The mass flow rate corresponding to each level of inlet subcooling was recorded. The pressure at capillary inlet for all experimental runs was maintained constant at 740 kPa. The internal surface roughness of the capillary tubes was measured using Surface Profilometer. For the measurement of surface roughness, a piece of capillary tube was sliced into two halves. The roughness for the capillary tubes of diameters 1.12 mm, 1.40 mm and 1.63 mm was found to be 7.05 mm, 6.22 mm and 3.58 mm, respectively. The capillary tube diameters and the pressure tap diameters were measured with the help of Tool maker’s microscope. The internal diameters of the capillary tubes are 1.12 mm, 1.40 mm and 1.63 mm, respectively. The uncertainty in the measurement of capillary tube diameters was 0.01 mm, capillary tube lengths 0.1 mm and surface roughness is 0.01 mm. Similarly, uncertainties in the measurement of pressure was 3.5 kPa in case of pressure gauges and 0.25% full scale (2.6 kPa) in case of pressure transducers while uncertainty in the measurement of temperature using T-type thermocouple was 0.1 C. The uncertainty in the
Table 1 – Range of input parameters Parameters
Selected range Straight capillary tube Instrumented
d (mm) L (m)a e/d p (mm) DTsub ( C) Pin (kPa)
1.12, 1.40, 1.63 6.4–2.4 0.0063, 0.0044, 0.0022 – 0–20 740
Non-instrumented 1.40 6.4–2.4 0.0044 – 0–20 740
Spiral capillary tube Instrumented 1.12, 1.40, 1.63 6.4–2.4 0.0063, 0.0044, 0.0022 20, 40, 60 0–20 740
a A total of six capillary lengths, viz., 6.4 m, 5.6 m, 4.8 m, 4.0 m, 3.2 m, 2.4 m, have been used for each test-section.
Non-instrumented 1.40 6.4–2.4 0.0044 40 0–20 740
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international journal of refrigeration 31 (2008) 970–978
Results and discussion
First of all, a comparison of experimental results of straight capillary tube with the correlation of Melo et al. (1999) has been made to check the integrity of the experimental set-up. Melo et al. (1999) correlation for mass flow rate of R-134a is given below: p0:552 p0:178 p5 ¼ 0:125p0:460 1 2 3
A comparison of experimental results of straight capillary tube has been made with those predicted by the widely accepted Melo et al. (1999) correlation to establish the integrity of present experimental set-up. Fig. 4 has been drawn taking measured experimental refrigerant mass flow rate in a straight capillary tube as abscissa and that predicted by Melo et al. (1999) correlation for the present experimental input conditions as ordinate. It has been found that Melo et al. (1999) correlation overpredicts the experimental data of both instrumented (with pressure taps) and non-instrumented (without pressure taps) straight capillary tubes in an error band of 0 to þ20%. Further, more than 75% data are in agreement with Melo et al. (1999) correlation in the error band of 0 to þ15%. It is to be noted that Melo et al. (1999) correlation has predicted their own experimental data in an error band of 15%. Therefore, it can be concluded that the data acquired from the present experimental set-up are in good agreement with predictions of Melo et al. (1999) correlation. This establishes the integrity of experimental set-up. In order to show the effect of pressure taps on the mass flow rate, the results of straight and spiral capillary instrumented and non-instrumented capillary tubes have been shown in Fig. 5. It is observed that the provision of taps for the measurement of pressure does not have any significant effect on the mass flow rate through the capillary tube as the deviation in mass flow rate in instrumented is less than 1%. The uncertainty in the refrigerant flow measurement is also 1%. Therefore, any conclusion regarding the effect of pressure taps on the refrigerant mass flow rate cannot be drawn. The
20 15 10
Length, L, m 5
6.4 5.6 4.8 4.0 3.2 2.4
non-instrumented instrumented
25 Pin d p e
20
spiral
740 kPa 1.40 mm 40 mm 6.22 μm
15 10 Length, L, m 5
6.4
5.6
4.8 4.0
3.2
2.4
non-instrumented instrumented
0 0
5
10
15
20
25
inlet subcooling, Tsub, °C Fig. 5 – Comparison of the mass flow rate for straight and coiled instrumented and non-instrumented capillary tubes.
insignificant effect of pressure taps on mass flow rate is due to the fact that the pressure tap area is very small in comparison to the internal surface area of the capillary tube and the flow passes near the taps almost undisturbed as a flexible boundary is formed at the location of tap as the refrigerant in the lines connecting taps to pressure header is stagnant. Since, cut-and-try method has been employed to carry out the investigation, for each cut of length, the corresponding mass flow rate has been recorded for different inlet subcoolings. Fig. 6 has been drawn with length of capillary as abscissa
40
25 coil pitch, mm
+20%
mass flow rate, m, kg h-1
predicted mass flow rate, kg h-1
straight Pin 740 kPa d 1.40 mm e 6.22 μm
0
(2)
mass flow rate, m, kg h-1
3.
25
mass flow rate, m, kg h-1
measurement of mass flow rate was 1% full scale (0.5 kg h1). All the instruments were calibrated prior to installation.
30
20
instrumented (with pressure taps) non-instrumented ( without pressure taps)
10
0
20 40 60 straight
20
15 d = 1.63 mm 10
d = 1.40 mm d = 1.12 mm
5
0 0
10
20
30
40
measured mass flow rate, kg h-1 Fig. 4 – Comparison of mass flow rate predicted by Melo et al. (1999) correlation with the measured mass flow rate.
2
3
4
5
6
capillary tube length, L, m Fig. 6 – Effect of coil pitch and capillary tube length on refrigerant mass flow rate.
7
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international journal of refrigeration 31 (2008) 970–978
and refrigerant mass flow rate as ordinate for the inlet subcoolings of refrigerant being in the range of 0–0.5 C. For the sake of comparison the straight tube data have also been plotted. The refrigerant mass flow rate rises with the increase in coil pitch and becomes highest for straight capillary tube. The best fit lines for straight and 20 mm pitch spiral capillary tubes have been drawn to quantify the effect of coiling. It has been observed that the mass flow rate is reduced in the range of 5–10% for all lengths of capillary tube. In fact, the coiling effect is pronounced for higher capillary tube diameters. The reason for the increase in mass flow rate with the increasing coil pitch is that increasing pitch leads to straightening of the capillary tube. The mass flow rate is highest for straight capillary tube as the straight capillary tube offers least resistance to the refrigerant flow. Further, it can be seen from the figure that the refrigerant mass flow rate increases with
reduction in capillary tube length, i.e., when the length is reduced from 6.4 m to 2.4 m, the mass flow rate is increased by 45%, 55% and 60% for tube diameters of 1.12 mm, 1.40 mm and 1.63 mm, respectively. Also, the mass flow rate increases tremendously with the small increase in tube diameter, i.e., as the tube diameter is increased from 1.12 mm to 1.63 mm, the mass flow is increased by 150% and 180% for capillary lengths of 6.4 m and 2.4 m, respectively. As per Darcy– Weisbach equation for pipe flow (Douglas et al., 1995), the pressure drop in a pipe is directly proportional to pipe length and inversely proportional to fifth power of pipe diameter. This fact also finds agreement with the experimental results. The cumulative effect of coil pitch, capillary tube diameter, the inlet subcooling and capillary tube length on the refrigerant mass flow rate has been presented in Fig. 7. It can be observed that with a slight increase in capillary tube diameter,
40
40 20 60
30
L = 6.4 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
coil pitch, mm 40 straight
d = 1.63 mm
20
d = 1.40 mm
10
d = 1.12 mm 0
coil pitch, mm 20 60
30
20
d = 1.63 mm d = 1.40 mm
10
d = 1.12 mm 0
0
5
10
15
20
25
0
5
inlet subcooling, ΔTsub,°C
15
20
25
40 coil pitch, mm 20 60
30
L = 4.8 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
10
inlet subcooling, ΔTsub,°C
40 40 straight
20
d = 1.63 mm d = 1.40 mm
10 d = 1.12 mm 0
coil pitch, mm 30
L = 4.0 m
40 straight
20 60
d = 1.63 mm 20 d = 1.40 mm 10 d = 1.12 mm 0
0
5
10
15
20
0
25
5
inlet subcooling, ΔTsub,°C
10
15
20
25
inlet subcooling, ΔTsub,°C
40
40 coil pitch, mm 20 60
30
L = 3.2 m
mass flow rate, m, kg h-1
mass flow rate, m, kg h-1
L = 5.6 m
40 straight
40 straight d = 1.63 mm
20 d = 1.40 mm 10 d = 1.12 mm
coil pitch, mm 20 60
30
L = 2.4 m
40 straight
d = 1.63 mm
20 d = 1.40 mm 10
d = 1.12 mm
0
0 0
5
10
15
20
inlet subcooling, ΔTsub,°C
25
0
5
10
15
20
inlet subcooling, ΔTsub,°C
Fig. 7 – Variation of mass flow rate with capillary length, diameter, pitch and inlet subcooling.
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In the above equation, the total number of variables is nine (N ¼ 9), out of which four variables, viz., d, rf, mf and cp are fixed as repeating variables, i.e. (M ¼ 4). Buckingham-p theorem (Douglas et al., 1995) states that the number of non-dimensional p-terms will be the difference between the total number of
Table 2 – Non-dimensional parameters p-Group Definition Description Relative uncertainty ðdp pÞ p1
d2 rf Pin m2f
p2
L Geometry effect d d2 r2f cp DTsub Inlet subcooling m2f
0.1564
p4
p d
Effect of coiling
0.0071
p5
m dmf
Mass flow rate
p3
Inlet pressure
0.0176
0.0186
parameters and the number of repeating variables, i.e. (N M ¼ 5). By performing the dimensional analysis, all the five p-terms and uncertainties associated with each p-term have been mentioned in Table 2. Eq. (3) in non-dimensional form can be represented as follows: p5 ¼ f2 ðp1 ; p2 ; p3 ; p4 Þ
(4)
Eq. (4) can be further expressed in a non-linear power law form as p5 ¼ Cpc11 pc22 pc33 F
(5)
where C is a constant and F is the coiling factor. Regression analysis of 275 data sets of coiled capillary tube and 103 data sets of straight capillary tube has resulted into the following correlation: p0:503 p0:126 F p5 ¼ Cp0:464 1 2 3
(6)
For straight capillary tube C ¼ 0.3478, F ¼ 1 and for spiral . capillary tube C ¼ 0.2607 and F ¼ p0:0393 4 In order to compare the predicted mass flow rate by the proposed correlation with the measured mass flow rate, Fig. 8 has been drawn. The mass flow rate predicted by Eq. (6) is in good agreement with the experimental mass flow rate as 85% of the straight capillary tube mass flow rate data lies in an error band of 10%. While, in case of coiled tube the same correlation predicts 90% of the mass flow rate in the error band of 10%. In Fig. 9, the proposed correlation for straight capillary tube has been compared with already established correlations of Melo et al. (1999) and Wolf et al. (1995). Melo et al. (1999) correlation has already been shown in Eq. (2). Wolf et al. (1995) correlation for R-134a (30 data sets) with 5% agreement with their own experimental data given by p5 ¼ 0:0129ðp1 Þ0:492 ðp2 Þ0:387 ðp3 Þ0:187
(7)
The percentage deviation appearing in Fig. 9 is evaluated using the following equation: percentage deviation ¼
mpredicted mmeasured 100 mmeasured
(8)
Fig. 9 shows the deviation of mass flow rates predicted by Melo et al. (1999) correlation, Wolf et al. (1995) correlation and the 40
predicted mass flow rate, kg h-1
the refrigerant mass flow rate increases drastically. At 10 C inlet subcooling, when the diameter is increased from 1.12 mm to 1.63 mm the refrigerant mass flow rate is increased in range of 170 5% for all capillary tube lengths. At the same inlet subcooling of 10 C, as the capillary length is reduced from 6.4 m to 2.4 m, the refrigerant mass flow rate is increased in the range of 50 5% for all tube diameters. Similarly, if the inlet subcooling is increased from 0 C to 10 C, the refrigerant mass flow rate is increased in a range 45 2% for all capillary tube diameters, lengths and pitches. In fact, the length of liquid region increases with the rise in inlet subcooling. Since the pressure drop is less in liquid region as compared to that in the twophase region, the refrigerant mass flow rate increases with the rise in inlet subcooling. The refrigerant mass flow rate also increases with the coil pitch. It has been observed that lower the pitch lesser will be the refrigerant mass flow rate. For 10 C inlet subcooling, the refrigerant mass flow rate for 20 mm, 40 mm and 60 mm spiral capillary tubes in comparison to the straight capillary tube is reduced in a range of 5– 15%. This is due to the fact that friction factor decreases with the increase in coil pitch and is least for the straight tube. Furthermore, increasing the coil pitch reduces the curvature thereby decreasing the resistance to the refrigerant flow. All the available correlations in the literature are mostly derived for straight capillary tubes. The mass flow rate of refrigerant through the adiabatic spiral capillary tube depends upon the capillary tube diameter, length, coil pitch, roughness and the inlet subcooling. As the capillary tubes are available in a limited band of roughness, the roughness effect is ignored in the development of correlation. Therefore, the roughness is not considered in the development of the correlation. Other parameters like inlet pressure, the density, the viscosity and specific heat of the refrigerant have also an influence on the mass flow rate. The REFPROP 7.0 database (McLinden et al., 2002), has been used to determine the thermodynamic and transport properties of the refrigerant R-134a, appearing in Eq. (3). The mass flow rate can be represented as a function of all these parameters (3) m ¼ f1 Pin ; L; d; p; DTsub ; rf ; mf ; cp
+10
35 30
-10 25 20 15 10 straight spiral
5 0 0
5
10
15
20
25
30
35
measured mass flow rate, kg h-1 0.0133
Fig. 8 – Comparison of the predicted mass flow rate with the measured experimental mass flow rate.
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international journal of refrigeration 31 (2008) 970–978
pressure taps on the refrigerant mass flow rate in straight and spiral capillary tube as well. 2. Parametric study has been conducted for the mass flow rate of R-134a through the capillary tubes of straight and coiled geometry. The effect coiling on refrigerant causes the refrigerant mass flow rate to reduce by 5–15%. 3. The semi-empirical correlations to predict the refrigerant mass flow rate through straight as well as spiral capillary tube have been proposed.
percentage deviation, %
60 40 20 0 -20 proposed correlation Melo et al. [15] correlation Wolf et al. [19] correlation
-40
references
-60 0
5
10
15
20
25
30
35
40
measured mass flow rate, kg h-1 Fig. 9 – Comparison of the proposed correlation with Melo et al. (1999) and Wolf et al. (1995) correlations.
proposed correlation from the measured experimental mass flow rate. The refrigerant mass flow rate predicted by Melo et al. (1999) correlation lies in the error band of 0 to þ20%. Melo et al. (1999) correlation has been developed for range of operating parameters different from the present experimental investigation. The range of tube diameter for Melo et al. (1999) correlation is 0.66–1.05 mm while in the present case it is 1.12– 1.63 mm, range of length is 1.99–3.02 m while in this case it is 2.4–6.4 m and range of inlet subcooling is 0–16 C, whereas, for the present case it is 0–25 C. The range of inlet pressure for Melo et al. (1999) correlation is 900 kPa and 1100 kPa while in the present study the inlet pressure has been kept nearly constant at 740 kPa. Most importantly it is the internal tube roughness, which is really making this difference. The capillary tube internal tube roughness as used by Melo et al. (1999) experiments lies in the range of 0.7–1.1 mm, whereas, in the present case the roughness is in the range of 3.5– 7.1 mm was in the tube. Therefore, with such a large difference in the range of operating parameters overprediction of 5% is a fairly good proposition. Also, the present experimental investigation has been carried out on both instrumented and non-instrumented straight capillary tubes whereas Melo et al. (1999) correlation has been developed for non-instrumented straight capillary tube. On the other hand Wolf et al. (1995) correlation predicts the same in the error band of þ10 to þ38%. Such a large discrepancy may be because of the fact that Wolf et al. (1995) has been developed for four different refrigerants R-134a, R-22, R-410a and R-152a with only 30 data points of R-134a used in the development of Wolf et al. (1995) correlation.
4.
Conclusions
The following conclusions can be drawn from the present study: 1. The effect of taps on the mass flow rate through the capillary tube is insignificant. Virtually, there is no effect of
ASHRAE Handbook – Refrigeration, 2006. American Society of Heating, Refrigerating and Air-Conditioning Engineer Inc., p 26 (Chapter 44). Bolstad, M.M., Jordan, R.C., 1948. Theory and use of the capillary tube expansion device. Refrigerating Engineering, 519–523. Choi, J., Kim, Y., Kim, H.Y., 2003. A generalized correlation for refrigerant mass flow rate through adiabatic capillary tubes. International Journal of Refrigeration 26, 881–888. Douglas, J.F., Gasiorek, J.M., Swaffield, J.A., 1995. Fluid Mechanics. Addison-Wesley Longman Inc., Edinburgh, UK, 299 pp. Gorasia, J.N., Dubey, N., Jain, K.K., 1991. Computer aided design of capillaries of different configurations. ASHRAE Transactions (Part 1), 132–138. Ito, H., 1959. Friction factors for turbulent flow in curved pipes. Journal of Basic Engineering D81, 123–134. Kuehl, S.J., Goldschmidt, V.W., 1990. Steady flows of R-22 through capillary tubes: test data. ASHRAE Transactions, 719–728. Kim, S.G., Ro, S.T., Kim, M.S., 2002. Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners. International Journal of Refrigeration 25, 521–531. Khan, M.K., Kumar, R., Sahoo, P.K., September 2007. Flow characteristics of refrigerants flowing inside an adiabatic spiral capillary tube. HVAC&R Research ASHRAE 13 (5), 731–748. Mikol, E.P., 1963. Adiabatic single and two-phase flow in small bore tubes. ASHRAE Journal, 75–86. Mori, Y., Nakayama, W., 1967. Study on forced convective heat transfer in curved pipes (2nd report, turbulent region). International Journal of Heat Mass Transfer 10, 37–59. Melo, C., Ferreira, R.T.S., Neto, C.B., Goncalves, J.M., Mezavila, M. M., 1999. An experimental analysis of adiabatic capillary tube. Applied Thermal Engineering 19, 669–684. McLinden, M.O., Klein, S.A., Lemmon, E.W., 2002. REFPROPversion 7 – thermodynamic and transport properties of refrigerants and refrigerant mixtures. NIST Standard Reference Database. Park, C., Lee, S., Kang, H., Kim, Y., 2007. Experimentation and modeling of refrigerant flow through coiled capillary tube. International Journal of Refrigeration 30, 1168–1175. Valladares, G., 2007. Numerical simulation and experimental validation of coiled adiabatic capillary tubes. Applied Thermal Engineering 27, 1062–1071. Wolf, D.A., Bittle, R.R., Pate, M.B., 1995. Adiabatic capillary tube performance with alternative refrigerants. ASHRAE Research Project RP-762. Zhou, G., Zhang, Y., 2006a. Numerical and experimental investigations on the performance of coiled adiabatic capillary tube. Applied Thermal Engineering 26, 1106–1114. Zhou, G., Zhang, Y., 2006b. Experimental investigation on hysteresis effect of refrigerant flowing through a coiled adiabatic capillary tube. Energy Conversion and Management 47, 3084–3093.